How do you find the surface normal of a sphere?
How to parameterize a normal vector to a sphere?
- Normal Vector to a Sphere. Consider a unit-radius sphere centered at the origin. One can parameterize it using the following: P (ϕ,θ) = (sin (ϕ)cos (θ), sin (ϕ)sin (θ), cos (ϕ)) My Vector Calculus book says that the Vector Product between the two partial derivates of the parameterized surface gives a Normal Vector to the surface.
Is the vector normal to the surface but not normalized?
- Your vector N → is indeed normal to the surface, but it's not normalized: This is a typical example of singular point (s) arising from the parametrization, they are called the artificial singularities. then it indeed is a normal vector (un-normalized) to the surface S. Now:
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